Asymptotic limits of \(\rho (\xi , x_1)\)  have been derived for the cases where \(A\)  is an i.i.d. Gaussian matrix [1]}, [2]} or a subsampled random orthogonal matrix [3]}. In our experiment, we consider the latter setting. Assume \(m = \lfloor \alpha n \rfloor \)  for some \(\alpha > 1\) . We can write
\(A= \begin{bmatrix}I_n & 0_{n \times (m-n)}\end{bmatrix} Q,\) 
